Method and device for reconstructing CT image and storage medium

ABSTRACT

A method and device for reconstructing a CT image and a storage medium are disclosed. CT scanning is performed on an object to be inspected to obtain projection data. The projection data is processed using a first convolutional neural network to obtain processed projection data. The first convolutional neural network comprises a plurality of convolutional layers. A back-projection operation is performed on the processed projection data to obtain a reconstructed image.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims priority to the Chinese Patent Application No.201710616651.7, filed on Jul. 25, 2017, which is incorporated herein byreference in its entirety.

TECHNICAL FIELD

The embodiments of the present disclosure relate to radiation imaging,and more particularly, to a method and device for reconstructing a CTimage and a storage medium.

BACKGROUND

X-ray CT imaging systems have been widely used in fields such as medicaltreatment, security inspection, industrial non-destructive detection,etc. Ray sources and detectors collect a series of projection dataaccording to a certain trajectory, and a three-dimensional spatialdistribution of linear attenuation coefficients of an object to beinspected may be obtained through recovery by using an imagereconstruction algorithm. A CT image reconstruction process is torecover a linear attenuation coefficient distribution from data acquiredby the detectors, which is a core step of CT imaging. Currently,analytical reconstruction algorithms such as filtered back-projection,Feldkmap-Davis-Kress (FDK), etc. and iterative reconstruction methodssuch as Algebra Reconstruction Technique (ART), Maximum A Posterior(MAP), etc. are mainly used in practical applications.

With the increasing diversity of demands for X-ray CT imaging, therequirements for reducing a radiation dosage have become higher andhigher, and the image quality which can be achieved by thereconstruction methods in the related art has approached the limit.There is a need to develop a new CT image reconstruction technique.

SUMMARY

In order to address one or more problems in the related art, there areprovided a method and a device for reconstructing a CT image and astorage medium, which can improve the quality of the reconstructedimage.

According to an aspect of the present disclosure, there is provided amethod for reconstructing a Computed Tomography (CT) image, comprising:performing CT scanning on an object to be inspected to obtain projectiondata; processing the projection data by using a first convolutionalneural network to obtain processed projection data, wherein the firstconvolutional neural network comprises a plurality of convolutionallayers; and performing a back-projection operation on the processedprojection data to obtain a reconstructed image.

According to some embodiments of the present disclosure, the CT scanningis one of the following: detector under-sampling scanning, sparse-anglescanning, intra-reconstruction scanning, finite angle scanning, andlinear trajectory scanning, and the first convolutional neural networkis a pooling layer-free convolutional neural network.

According to some embodiments of the present disclosure, the CT scanningis circular scanning or helical scanning, and the first convolutionalneural network further comprises a plurality of pooling layers disposedafter respective convolutional layers, and a fully connected layer.

According to some embodiments of the present disclosure, the methodfurther comprises a step of: processing the reconstructed image by usinga second convolutional neural network to obtain the resultant image.

According to some embodiments of the present disclosure, the methodfurther comprises a step of: before processing the projection data byusing a first convolutional neural network, filtering the projectiondata by using a ramp filter.

According to some embodiments of the present disclosure, thereconstructed image is locally smoothed by using the secondconvolutional neural network to obtain the resultant image.

According to some embodiments of the present disclosure, a convolutionalkernel of a convolutional layer in the first convolutional neuralnetwork has a dimension of a detector pixel sequence and anotherdimension of a scanning angle, and a scale of the convolutional kernelof the convolutional layer in the first convolutional neural network onthe dimension of the detector pixel sequence is set independently from ascale of the convolutional kernel of the convolutional layer in thefirst convolutional neural network on the dimension of the scanningangle.

According to some embodiments of the present disclosure, the scale ofthe convolutional kernel of the convolutional layer (for example, afirst convolutional layer) in the first convolutional neural network onthe dimension of the detector pixel sequence is greater than the scaleof the convolutional kernel of the convolutional layer in the firstconvolutional neural network on the dimension of the scanning angle.

According to some embodiments of the present disclosure, the firstconvolutional neural network comprises at least three convolutionallayers, each of which has an activation function for performing anon-linear operation on projection data processed by the convolutionallayer.

According to some embodiments of the present disclosure, the firstconvolutional neural network further comprises a back-projection layerfor performing a back-projection operation on projection data processedby the convolutional layer.

According to some embodiments of the present disclosure, a length-widthsize parameter of a convolutional kernel of a convolutional layer in thefirst convolutional neural network which is closest to theback-projection layer is 1*1.

According to some embodiments of the present disclosure, the secondconvolutional neural network comprises an image domain initialconvolutional layer and an end convolutional layer for processing thereconstructed image in an image domain.

According to some embodiments of the present disclosure, eachconvolutional layer included in the image domain initial convolutionallayer has an activation function, and the end convolutional layer has noactivation function.

According to another aspect of the present disclosure, there is provideda device for reconstructing a Computed Tomography (CT) image,comprising: a CT scanning apparatus configured to perform CT scanning onan object to be inspected to obtain projection data; a processorconfigured to: process projection data by using a first convolutionalneural network to obtain processed projection data, and perform aback-projection operation on the processed projection data to obtain areconstructed image, wherein the first convolutional neural networkcomprises a plurality of convolutional layers.

According to some embodiments of the present disclosure, the CT scanningapparatus is configured to perform one of the following: detectorunder-sampling scanning, sparse-angle scanning, intra-reconstructionscanning, finite angle scanning, and linear trajectory scanning, and thefirst convolutional neural network is a pooling layer-free convolutionalneural network.

According to some embodiments of the present disclosure, the CT scanningapparatus is configured to perform circular scanning or helicalscanning, and the first convolutional neural network further comprises aplurality of pooling layers disposed after respective convolutionallayers, and a fully connected layer.

According to some embodiments of the present disclosure, the processoris further configured to: process the reconstructed image by using asecond convolutional neural network to obtain the resultant image.

According to some embodiments of the present disclosure, the processoris further configured to: locally smooth the reconstructed image byusing the second convolutional neural network to obtain the resultantimage.

According to yet another aspect of the present disclosure, there isprovided a computer-readable medium having computer programs storedthereon, which when being executed by a processor, cause the processorto perform the following steps: processing projection data by using afirst convolutional neural network to obtain processed projection data,wherein the projection data is obtained by performing CT scanning on anobject to be inspected; and performing a back-projection operation onthe processed projection data to obtain a reconstructed image.

With the solutions according to the embodiments of the presentdisclosure described above, a CT image with a higher quality can bereconstructed.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS

For better understanding of the present disclosure, the presentdisclosure will be described in detail with reference to the followingaccompanying drawings:

FIG. 1 illustrates a schematic structural diagram of a device forreconstructing a CT image according to an embodiment of the presentdisclosure;

FIG. 2 is a schematic structural diagram of a control and reconstructionapparatus in the device shown in FIG. 1;

FIG. 3 illustrates an example of a sinogram of projection data obtainedby the device according to an embodiment of the present disclosure;

FIG. 4 illustrates a schematic structural diagram of a convolutionalnetwork used in the device according to an embodiment of the presentdisclosure;

FIG. 5 illustrates a schematic structural diagram of a convolutionalneural network used in the device according to an embodiment of thepresent disclosure;

FIGS. 6A, 6B, and 6C illustrate a diagram of sizes of filter cores usedin the device according to an embodiment of the present disclosure;

FIG. 7 is a schematic flowchart illustrating a method according to anembodiment of the present disclosure;

FIG. 8 is a schematic diagram of a scanning apparatus which implementslimited-angle CT scanning according to another embodiment of the presentdisclosure;

FIG. 9 is a schematic diagram of a scanning apparatus which implements asparse-angle sampling scanning method according to yet anotherembodiment of the present disclosure;

FIG. 10 is a schematic diagram of a scanning apparatus which implementsan intra-reconstruction scanning method according to yet anotherembodiment of the present disclosure;

FIG. 11 is a schematic diagram of a scanning apparatus which implementsa detector under-sampling scanning method according to yet anotherembodiment of the present disclosure;

FIG. 12 illustrates a schematic diagram of data contained in sinogramsin the different scanning modes shown in FIGS. 8, 9, 10, and 11; and

FIG. 13 illustrates a schematic diagram of a scanning apparatus whichimplements linear trajectory CT scanning according to yet anotherembodiment of the present disclosure.

DETAILED DESCRIPTION

The specific embodiments of the present disclosure will be described indetail below. It should be noted that the embodiments herein are usedfor illustration only, without limiting the present disclosure. In thedescription below, a number of specific details are explained to providebetter understanding of the present disclosure. However, it is apparentto those skilled in the art that the present disclosure can beimplemented without these specific details. In other instances, wellknown circuits, materials or methods are not described specifically soas not to obscure the present disclosure.

Throughout the specification, the reference to “one embodiment,” “anembodiment,” “one example” or “an example” means that the specificfeatures, structures or properties described in conjunction with theembodiment or example are included in at least one embodiment of thepresent disclosure. Therefore, the phrases “in one embodiment,” “in anembodiment,” “in one example” or “in an example” occurred in variouspositions throughout the specification may not necessarily refer to thesame embodiment or example. Furthermore, specific features, structuresor properties may be combined into one or more embodiments or examplesin any appropriate combination and/or sub-combination. Moreover, itshould be understood by those skilled in the art that the term “and/or”used herein means any and all combinations of one or more listed items.

For one or more problems in the related art, the embodiments of thepresent disclosure provide a method and device for reconstructing a CTimage and a storage medium. According to the embodiments of the presentdisclosure, projection data (displayed as a sinogram, with a dimensionbeing a detector pixel sequence, and another dimension being a scanningangle) obtained through CT scanning is processed by using aconvolutional neural network, to obtain processed projection data (forexample, a sinogram with enhanced characteristics in a projectiondomain). Then, the processed projection data is back-projected to obtaina CT image. In this way, the quality of the CT image can be improved,and particularly, a CT image with a higher quality can be reconstructedeven in a case that projection data is incomplete due to detectorunder-sampling, sparse-angle scanning, intra-reconstruction,limited-angle scanning, or linear trajectory scanning, etc. In otherembodiments, the CT image may further be processed by using anotherconvolutional neural network, to obtain a final image.

FIG. 1 illustrates a schematic structural diagram of a device forreconstructing a CT image according to an embodiment of the presentdisclosure. As shown in FIG. 1, the CT device according to the presentembodiment comprises an X-ray source 10, a mechanical movement apparatus50, a detector and data acquisition system 20, and a control andreconstruction apparatus 60, so as to perform CT scanning andreconstruction on an object 40 to be inspected.

The X-ray source 10 is, for example, an X-ray machine, and anappropriate focus size of the X-ray machine is selected according to aresolution of imaging. In other embodiments, instead of using the X-raymachine, an X-ray beam may be generated by using a linear accelerator.

The mechanical movement apparatus 50 comprises a stage, a rack, acontrol system, etc. The stage may be translated to adjust a position ofa center of rotation. The rack may be translated to align the X-raysource (the X-ray machine) 10, the detector, and the center of rotation.In the present embodiment, the description is made according to acircular scanning trajectory or a spiral trajectory of a rotationalstage and a fixed rack. As the movement of the stage with respect to therack is a relative motion, the method according to the presentembodiment may also be implemented by a fixed stage and a rotationalrack.

The detector and data acquisition system 20 comprises an X-ray detector,a data acquisition circuit, etc. A solid detector, a gas detector, orother detectors may be used as the X-ray detector; however, theembodiments of the present disclosure are not limited thereto. The dataacquisition circuit comprises a readout circuit, an acquisition triggercircuit, a data transmission circuit, etc.

The control and reconstruction apparatus 60 comprises, for example, acomputer device installed with a control program and a reconstructionprogram, and is responsible for performing control of an operationprocess of the CT system, including mechanical rotation, electricalcontrol, safety interlock control, etc., and reconstructing a CT imagefrom the projection data.

FIG. 2 illustrates a schematic structural diagram of the control andreconstruction apparatus shown in FIG. 1. As shown in FIG. 2, datacollected by the detector and data acquisition system 20 is stored in astorage device 61 through an interface unit 67 and a bus 68. A Read-OnlyMemory (ROM) 62 has configuration information and programs of a computerdata processor stored therein. A Random Access Memory (RAM) 63 isconfigured to temporarily store various data during operation of aprocessor 65. In addition, computer programs for performing dataprocessing, such as a calculation program for reconstructing a CT image,are also stored in the storage device 61. The storage device 61, theread-only memory 62, the random access memory 63, an input apparatus 64,the processor 65, a display device 66, and the interface unit 67 areconnected through the internal bus 68.

After a user inputs an operation command through the input apparatus 64such as a keyboard, a mouse, etc., instruction codes of the computerprogram instruct the processor 65 to execute an algorithm forreconstructing a CT image, and after obtaining a reconstruction result,display the reconstruction result on the display device 66 such as anLCD display, or output a processing result directly in a form of a hardcopy such as printing.

According to an embodiment of the present disclosure, CT scanning isperformed on an object to be inspected by using the above device toobtain projection data. Generally, such projection data may be displayedin a form of a two-dimensional image. FIG. 3 illustrates an example ofprojection data obtained according to an embodiment of the presentdisclosure. A horizontal axis of the sinogram shown in FIG. 3 representsa detector pixel sequence (for example, from 1 to 256) and a verticalaxis of the sinogram shown in FIG. 3 represents an angle (for example,from 1 degree to 360 degrees). The processor 65 in the control devicethen executes a reconstruction program to process projection data byusing a first convolutional neural network to obtain processedprojection data, and perform a back-projection operation on theprocessed projection data to obtain a reconstructed image.

As described above, in the embodiments of the present disclosure,projection data is processed by using a convolutional neural network ina projection domain, then a back-projection operation is performed toreconstruct a CT image. The convolutional neural network may compriseconvolutional layers, pooling layers, and fully connected layers. Theconvolutional layers each identify characteristics of an input data set,and each convolutional layer has a nonlinear activation functionoperation. The characteristics is refined by the pooling layers, andtypical operations comprise mean-pooling and max-pooling. One or morefully connected layers implement a high-order signal nonlinear synthesisoperation, and the full connected layer also has a nonlinear activationfunction. The commonly used nonlinear activation functions compriseSigmoid, Tanh, ReLU, etc.

FIG. 4 illustrates a schematic structural diagram of a convolutionalnetwork used in the device according to an embodiment of the presentdisclosure. As shown in FIG. 4, the Convolutional Neural Network (CNN)may be formed by stacking different layers, which may transform inputdata into output data. For example, the projection data (for example, asinogram 410 shown in FIG. 4) obtained through CT scanning is processedto obtain processed projection data (for example, a processed sinogram450 shown in FIG. 4).

The convolutional neural network shown in FIG. 4 comprises a pluralityof convolutional layers, for example, a first convolutional layer 420, asecond convolutional layer 430, . . . , an (n+1)^(th) convolutionallayer 440, where n is a natural number. These convolutional layers areessential blocks of the CNN. Parameters of each convolutional layerconsist of a set of learnable convolutional kernels (or simply calledconvolutional kernels), each of which has a certain receptive field andextends over the entire depth of the input data. In a forward process,each convolutional kernel is convolved along a width and a height of theinput data, a dot product of elements of the convolutional kernel andthe input data is calculated, and a two-dimensional activation map ofthe convolutional kernel is generated. As a result, the network maylearn a convolutional kernel which can be activated only when a specifictype of characteristics is seen at a certain input spatial position.

Activation maps of all the convolutional kernels are stacked in a depthdirection to form all the output data of the convolutional layer.Therefore, each element in the output data may be interpreted as anoutput of a convolutional kernel which sees a small area in the inputand shares parameters with other convolutional kernels in the sameactivation map.

For example, the input projection data obtained by CT scanning isg={g₁,g₂,L,g_(M)}, a line integral projection process isH={H_(mn)}_(M×N), and the output is a reconstructed image f.

The first convolutional layer 420 implements the following operation:g⁽¹⁾=g⊗c⁽¹⁾≡(C⁽¹⁾)^(T)g, where C⁽¹⁾ represents a convolutional kernel,and T represents “transpose.” A two-dimensional convolutional kernel ona certain scale has two dimensions, a first one of which is defined as adetector pixel sequence, and a second one of which is defined as ascanning angle here. Lengths of the convolutional kernel in the twodimensions do not need to be the same. Generally, a scale of theconvolutional kernel C⁽¹⁾ on the dimension of the detector pixelsequence is set to be greater than a scale of the convolutional kernelC⁽¹⁾ on the dimension of the scanning angle, for example, 3*1, 5*1, and5*3 convolutional kernels are used, as shown in FIGS. 6A, 6B and 6C. Aplurality of convolutional kernels may be set on each scale. A scale ofa convolutional kernel of a convolutional layer in a convolutionalneural network on the dimension of the detector pixel sequence is setindependently from a scale of the convolutional kernel of theconvolutional layer in the convolutional neural network on the dimensionof the scanning angle. The convolutional layer has an activationfunction φ(g⁽¹⁾). K⁽¹⁾ is defined as a thickness of this layer, i.e. anumber of convolutional kernels. K⁽¹⁾ new sinograms are formed for thislayer. In FIG. 4, a thickness of the first convolutional layer 420 is 3(i.e., the first convolutional layer 420 has 3 convolutional kernels),wherein all the convolutional kernels are network parameters to bedetermined. These network parameters are obtained by training theconvolutional neural network. The thickness of 3 in FIG. 4 is merely anexample, and the present disclosure is not limited thereto. By takingthe reconstruction of two-dimensional parallel beam CT scanning as anexample, 24 convolutional kernels may be set for one convolutionallayer, so that 24 sinograms are obtained for a first layer of thenetwork. ReLU is selected as the activation function. ReLU is anabbreviation for a Rectified Linear Unit. This is a neuron layer towhich a non-saturated activation function ƒ(x)=max(0,x) is applied. Adecision function and non-linear characteristics of the entire networkare added without affecting the receptive field of the convolutionallayer.

A plurality of convolutional layers similar to the first convolutionallayer may be set, with a thickness of each convolutional layer beingK^((n)).

The second convolutional layer 430 is similar to the first convolutionallayer 420, and a thickness of the second convolutional layer is K⁽²⁾.For example, a sinogram output by a previous convolutional layer isfurther processed by using C^((n)). As shown in FIG. 4, the thickness ofthe second convolutional layer 430 is 3, wherein all the convolutionalkernels are network parameters to be determined. These networkparameters are obtained by training the convolutional neural network.The above-mentioned 3 is merely an example. Similarly, 24 convolutionalkernels may be set for one convolutional layer, so that 24 sinograms areobtained for the second convolutional layer (a second layer of thenetwork). Here, ReLu is selected as the activation function. In anotherembodiment, a convolution operation is performed in a thicknessdirection in the second convolutional layer by using a convolutionalkernel having a shape/size parameter of 18*1*1 to obtain an output ofthe second layer, with ReLu being the activation function.

The (n+1)^(th) convolutional layer 440 may be, for example, an(n+1)^(th) layer of the network, specifically an (n+1)^(th)convolutional layer, and there may be or may not be anotherconvolutional layer between the second convolutional layer 430 and the(n+1)^(th) convolutional layer 440. The (n+1)^(th) convolutional layer440 implements the following operation:g^((n+1))=g^((n))⊗c^((n+1))≡(C^((n+1)))^(T)g^((n)), where C^((n+1))represents a convolutional kernel and T represents “transpose.” Aconvolutional kernel of the (n+1)^(th) convolutional layer has ashape/size parameter of K^((n+1))×1×1 a thickness of K^((n+1)), and alength and a width each being 1. A sinogram output by a previousconvolutional layer is further processed, to obtain the processedsinogram. This convolutional layer also has an activation functionϕ(g^((n+1))).

The convolutional neural network as shown in FIG. 4 further comprises aback-projection layer 460. The back-projection layer 460 is, forexample, an (n+2)^(th) layer of the convolutional neural network andimplements the following operation: f^((n+2))=H^(T)g^((n+1)), i.e.,performing a CT back-projection operation, and weight coefficientsbetween network nodes are determined by a geometric relationship of theCT scanning device. There are no parameters to be determined for thislayer. As another manner, a projection matrix H may be determined basedon the geometric relationship of the CT scanning device, and aback-projection operation may be performed on the processed sinogram toobtain a reconstructed CT image. For example, the projection matrix iscalculated by using an Siddon method, and elements of the system matrixcorrespond to connection weights of a back-projection connection layer.

FIG. 5 illustrates a schematic structural diagram of anotherconvolutional network used in the device according to an embodiment ofthe present disclosure. As shown in FIG. 5, an input projection data510, a convolutional layer 520, a convolutional layer 530, and aconvolutional layer 540 are similar to the input sinogram 410, the firstconvolutional layer 420, the second convolutional layer 430 and the(n+1)^(th) convolutional layer 440 shown in FIG. 4, and will not berepeated here. The structure shown in FIG. 5B differs from that shown inFIG. 5 in that in the structure shown in FIG. 5B, a second convolutionalneural network is further provided, which comprises an image domaininitial convolutional layer (one convolutional layer 570 is shown inFIG. 5 as an example, but the present disclosure is not limited thereto)and an end convolutional layer (a convolutional layer 580), and thereconstructed CT image is processed in the image domain, for example, islocally smoothed, to output the resultant image.

For example, if the image domain initial convolutional layer comprisesonly one convolutional layer 570, the convolutional layer 570 describedabove may be represented as f^((n′))=(C^((n′)))^(T)f^((n+2)). If theimage domain initial convolutional layer comprises a plurality ofconvolutional layers, a convolutional layer following a firstconvolutional layer in the image domain initial convolutional layer maybe represented as ƒ^((n+1′))=(C^((n+1′)))^(T)ƒ^((n′)), where f^((n′)) isan output of a previous convolutional layer. Each of these convolutionallayers in the image domain initial convolutional layer has an activationfunction φ(f^((k))). The output of the image domain initialconvolutional layer is input to the convolutional layer 580.

The convolutional layer 580 is a last but one layer of the network, andthe convolutional layer 580 implements the following operation:f^((*))=f^((*−1))⊗c^((*))≡(C^((*)))^(T)f^((*−1)), where ƒ^((*−1)) is anoutput of a previous convolutional layer (ƒ^((*−1)) is f(n′) in a casethat the image domain initial convolutional layer only comprises oneconvolutional layer 570), with a shape/size parameter of theconvolutional kernel being K^((*−1))×1×1, so as to obtain a resultantimage. Here, K^((*−1)) is a number of convolutional kernels of theprevious convolutional layer. That is, convolution occurs in thethickness direction. This convolutional layer has no activationfunction.

Although no pooling layer is included in the above structure, there maybe a pooling layer in the above structure. For example, in a case thatcomplete data is obtained by CT scanning (for example, full detector360-degree circular scanning), a pooling layer may be provided after oneor more convolutional layers. However, in a case that incomplete data isobtained by CT scanning (for example, detector under-sampling,sparse-angle sampling, limited-angle, intra-reconstruction, or lineartrajectory, etc.), no pooling layer is provided.

In addition, according to an embodiment of the present disclosure, thesecond convolutional neural network further comprises an output layerwhich is at the last layer of the network, and the output layer outputsthe resultant image. For the resultant image output by the output layer,a cost function is defined as Φ(f)=½(f−f*)^(T)W(f−f*), wheref={ƒ₁,ƒ₂,L,ƒ_(n)} is the output resultant image, f* is a target image,and W is a diagonal matrix for controlling weights. The parameters ofthe first convolutional neural network and the second convolutionalneural network are updated by making the cost function toward zero. In acase that the second convolutional neural network is not provided, thereconstructed image output by the first convolutional neural network istaken as the resultant image, and the parameters of the firstconvolutional neural network are updated based on the above costfunction.

In addition, ramp convolution may further be performed on a sinogramobtained by performing CT scanning using an RL ramp filter. It can beunderstood by those skilled in the art that other activation functionsmay also be used. For example, in some other embodiments, otherfunctions, such as a hyperbolic tangent function ƒ(x)=tanh(x) and aSigmoid function ƒ(x)=(1+e^(−x))⁻¹, may also be used to increase thenonlinearity. Compared with other functions, the ReLU function is morecommonly used as it allows a neural network to be trained several timesfaster without having a significant impact on the accuracy.

Methods such as a random gradient descent method, a momentum updatemethod, Nesterov Momentum, AdaGrad, Adam, etc. may be used to updatenetwork parameters. For example, back-propagation of an error is asfollows:

-   -   a) A gradient of an output layer is

${\frac{\partial{\Phi(f)}}{\partial f} = {\left( {f - f^{*}} \right)^{T}W}},$

-   -   b) Error propagation of a back-projection layer is

${\frac{\partial f^{(4)}}{\partial g} = H^{T}},$

-   -   c) Error propagation of a convolution operation of a        convolutional layer is

${\frac{\partial g^{(n)}}{\partial g^{({n - 1})}} = \lbrack C\rbrack^{T}},$

-   -   d) Error propagation of an activation function in each layer is        φ′(⋅), wherein, by taking φ(x)=max(0, x) as an example,        φ′(x)=u(x), which is a step function,    -   e) Update of network parameters using a stochastic gradient        descent method, a momentum update method, Nesterov Momentum,        AdaGrad, Adam, etc.,    -   f) Training using simulation data, and    -   g) Training using actual scanning data.

Specifically, after the convolutional neural network is established asabove, network parameters are trained. For example, a basic mathematicalmodel of a scanned object is established and CT simulation data isgenerated by modeling an actual system. In addition, according to anembodiment of the present disclosure, CT simulation data of a pluralityof scanned objects may further be used as an input of the network, andan image true value of the scanned objects is used as a marker, to trainthe network parameters. In other embodiments, the object is also scannedon the actual system, to obtain CT scanning data, which is input to thenetwork for reconstruction and testing. Targeted image processing isperformed on a test result, for example, known local smooth regions arelocally smoothed. The network is further trained by using the processedimage as a marker to achieve fine tuning of the network parameters.

FIG. 7 is a schematic flowchart illustrating a method according to anembodiment of the present disclosure. As shown in FIG. 7, in step S710,CT scanning is performed on the object to be inspected to obtainprojection data. The CT scanning here may be mono-energy scanning ormulti-energy scanning, and the embodiments of the present disclosure arenot limited thereto.

In step S720, the projection data is filtered by using a ramp filter.For example, the projection data is filtered by using an RL ramp filter.It can be understood by those skilled in the art that other filters maybe used here or filtering is not performed.

In step S730, the projection data is processed by using the firstconvolutional neural network 420/430/440 in a projection domain toobtain processed projection data. For example, the projection data isprocessed by by using a convolutional neural network obtained bytraining to obtain a processed sinogram, as shown in FIG. 4.

In step S740, a back-projection operation is performed on the processedprojection data. For example, a back-projection operation is performedin the back-projection layer 460 shown in FIG. 4 to obtain areconstructed CT image.

As described above, as another embodiment, post-processing may beperformed on the CT image after the CT image is obtained, for example,in step S750, the reconstructed CT image is processed by using thesecond convolutional neural network 570/580 to obtain the resultantimage. For example, the reconstructed image is locally smoothed or otherimage processing operations such as segmentation, edge enhancement, andequalization, etc. may be performed on the reconstructed image.

Although the above description is mainly described for a case that360-degree circular scanning is performed to obtain complete projectiondata, it can be understood by those skilled in the art that the abovesolution can be applied to the case of incomplete projection data dueto, for example, detector under-sampling, sparse-angle sampling,limited-angle, intra-reconstruction, or linear trajectory scanning, etc.

FIG. 8 is a schematic diagram of a scanning apparatus which implementslimited-angle CT scanning according to another embodiment of the presentdisclosure. As shown in FIG. 8, after X rays emitted by the radiationsource 10 pass through the object 40 to be inspected in a field of view45, the X rays are received by the detector 30, converted intoelectrical signals, further converted into digital signals indicatingattenuation values, and reconstructed in a computer as projection data.With the solutions described above, an image with a higher quality canbe reconstructed even if limited-angle (for example, 130-degree) CTscanning is performed on the object 40 to be inspected.

FIG. 9 is a schematic diagram of a scanning apparatus which implements asparse-angle sampling scanning method according to yet anotherembodiment of the present disclosure. As shown in FIG. 9, after X raysemitted by the radiation source 10 pass through the object 40 to beinspected in a field of view 45, the X rays are received by the detector30, converted into electrical signals, further converted into digitalsignals indicating attenuation values, and reconstructed in a computeras projection data. With the solutions described above, an image with ahigher quality can be reconstructed even if CT scanning at a number ofrotation positions (for example, six positions) is performed on theobject 40 to be inspected. In this way, an image with a higher qualitycan be reconstructed from the incomplete projection data even ifspare-angle CT scanning is performed on the object to be inspected.

FIG. 10 is a schematic diagram of a scanning apparatus which implementsan intra-reconstruction scanning method according to yet anotherembodiment of the present disclosure. As shown in FIG. 10, after X raysemitted by the radiation source 10 pass through a part of the object 40to be inspected in a field of view 45, the X rays are received by thedetector 30, converted into electrical signals, further converted intodigital signals indicating attenuation values, and reconstructed in acomputer as projection data. With the solutions described above, animage with a higher quality can be reconstructed even ifintra-reconstruction CT scanning is performed on the object 40 to beinspected.

FIG. 11 is a schematic diagram of a scanning apparatus which implementsa detector under-sampling scanning method according to yet anotherembodiment of the present disclosure. As shown in FIG. 11, after X raysemitted by the radiation source 10 pass through the object 40 to beinspected in a field of view 45, the X rays are received by the detector30, converted into electrical signals, further converted into digitalsignals indicating attenuation values, and reconstructed in a computeras projection data. In this example, the detector 30 is set to be in anunder-sampled form, for example, under-sampling is realized by spacingvarious detector units apart by a predetermined distance. In this way,with the solutions described above, an image with a higher quality canbe reconstructed even if detector under-sampling CT scanning isperformed on the object 40 to be inspected.

FIG. 12 is a schematic diagram illustrating incomplete projection datainvolved in the scanning modes shown in FIGS. 8, 9, 10, and 11. As shownin FIG. 12, the projection data obtained by sparse-angle sampling CTscanning, limited-angle CT scanning, detector under-sampling CTscanning, and intra-reconstruction CT scanning are all incomplete.Although the projection data is incomplete, with the above solutions, animage with a higher quality can be reconstructed from the incompleteprojection data.

Although methods such as sparse-angle sampling scanning are given above,it can be reached by those skilled in the art that the method accordingto the present disclosure may also be used in a linear trajectory CTscanning system. FIG. 13 illustrates a schematic diagram of a scanningapparatus which implements linear trajectory CT scanning according toyet another embodiment of the present disclosure.

As shown in FIG. 13, after X rays emitted by the radiation source 10pass through the object 40 to be inspected in a field of view, the Xrays are received by the detector 30, converted into electrical signals,further converted into digital signals indicating attenuation values,and reconstructed in a computer as projection data. In this example, theobject 40 to be inspected moves along a linear trajectory on a conveyorbelt parallel to the detectors. A field angle of the ray source formedby the detectors in a horizontal direction is as large as possible, andthe detectors cover the object in a vertical direction. For example, thedetector array is placed on an opposite side of the source, and ahorizontal field angle θ of the rays is required to be more than 90degrees, to obtain protection data through the linear trajectory CTscanning. With the solutions described above, an image with a higherquality can be reconstructed even if linear trajectory CT scanning isperformed on the object 40 to be inspected.

The embodiments of the present disclosure provide an X-ray CTreconstruction method based on a convolutional neural network to deeplymine data information, form a convolutional neural network andsystem-specific parameters, and obtain an efficient CT imagereconstruction method.

The method according to the present disclosure can be flexibly appliedto different CT scanning modes and system architectures and can be usedin the fields of medical diagnosis, industrial non-destructive detectionand security inspection.

The foregoing detailed description has set forth various embodiments ofthe method and device for reconstructing a CT image via the use ofdiagrams, flowcharts, and/or examples. In a case that such diagrams,flowcharts, and/or examples contain one or more functions and/oroperations, it will be understood by those skilled in the art that eachfunction and/or operation within such diagrams, flowcharts or examplesmay be implemented, individually and/or collectively, by a wide range ofstructures, hardware, software, firmware, or virtually any combinationthereof. In one embodiment, several portions of the subject matterdescribed in the embodiments of the present disclosure may beimplemented via Application Specific Integrated Circuits (ASICs), FieldProgrammable Gate Arrays (FPGAs), Digital Signal Processors (DSPs), orother integrated formats. However, those skilled in the art willrecognize that some aspects of the embodiments disclosed herein, inwhole or in part, may be equivalently implemented in integratedcircuits, as one or more computer programs running on one or morecomputers (e.g., as one or more programs running on one or more computersystems), as one or more programs running on one or more processors(e.g., as one or more programs running on one or more microprocessors),as firmware, or as virtually any combination thereof, and that designingthe circuitry and/or writing the code for the software and/or firmwarewould be well within the skill of those skilled in the art in ray ofthis disclosure. In addition, those skilled in the art will appreciatethat the mechanisms of the subject matter described herein are capableof being distributed as a program product in a variety of forms, andthat an illustrative embodiment of the subject matter described hereinapplies regardless of the particular type of signal bearing medium usedto actually carry out the distribution. Examples of a signal bearingmedium include, but are not limited to, the following: a recordable typemedium such as a floppy disk, a hard disk drive, a Compact Disc (CD), aDigital Versatile Disk (DVD), a digital tape, a computer memory, etc.;and a transmission type medium such as a digital and/or an analogcommunication medium (e.g., a fiber optic cable, a waveguide, a wiredcommunications link, a wireless communication link, etc.).

While the present disclosure has been described with reference toseveral typical embodiments, it is apparent to those skilled in the artthat the terms are used for illustration and explanation purpose and notfor limitation. The present disclosure may be practiced in various formswithout departing from the spirit or essence of the present disclosure.It should be understood that the embodiments are not limited to any ofthe foregoing details, and shall be interpreted broadly within thespirit and scope as defined by the following claims. Therefore, all ofmodifications and alternatives falling within the scope of the claims orequivalents thereof are to be encompassed by the claims as attached.

We claim:
 1. A method for reconstructing a Computed Tomography (CT)image, comprising: performing CT scanning on an object to be inspectedto obtain projection data; processing the projection data by using afirst convolutional neural network to obtain processed projection data,wherein the first convolutional neural network comprises a plurality ofconvolutional layers; performing a back-projection operation on theprocessed projection data to obtain a reconstructed image; andprocessing the reconstructed image by using a second convolutionalneural network to obtain a resultant image.
 2. The method according toclaim 1, wherein the CT scanning is one of the following: detectorunder-sampling scanning, sparse-angle scanning, intra-reconstructionscanning, finite angle scanning, and linear trajectory scanning, and thefirst convolutional neural network is a pooling layer-free convolutionalneural network.
 3. The method according to claim 1, wherein the CTscanning is circular scanning or helical scanning, and the firstconvolutional neural network further comprises a plurality of poolinglayers disposed after respective convolutional layers, and a fullyconnected layer.
 4. The method according to claim 1, further comprisinga step of: before processing the projection data by using a firstconvolutional neural network, filtering the projection data by using aramp filter.
 5. The method according to claim 1, wherein thereconstructed image is locally smoothed by using the secondconvolutional neural network to obtain the resultant image.
 6. Themethod according to claim 1, wherein a convolutional kernel of aconvolutional layer in the first convolutional neural network has adimension of a detector pixel sequence and another dimension of ascanning angle, and a scale of the convolutional kernel of theconvolutional layer in the first convolutional neural network on thedimension of the detector pixel sequence is set independently from ascale of the convolutional kernel of the convolutional layer in thefirst convolutional neural network on the dimension of the scanningangle.
 7. The method according to claim 6, wherein the scale of theconvolutional kernel of the convolutional layer in the firstconvolutional neural network on the dimension of the detector pixelsequence is greater than the scale of the convolutional kernel of theconvolutional layer in the first convolutional neural network on thedimension of the scanning angle.
 8. The method according to claim 1,wherein the first convolutional neural network comprises at least threeconvolutional layers, each of which has an activation function forperforming a non-linear operation on projection data processed by theconvolutional layer.
 9. The method according to claim 1, wherein thefirst convolutional neural network further comprises a back-projectionlayer for performing a back-projection operation on projection dataprocessed by the convolutional layer.
 10. The method according to claim9, wherein a length-width size parameter of a convolutional kernel of aconvolutional layer in the first convolutional neural network which isclosest to the back-projection layer is 1*1.
 11. The method according toclaim 1, wherein the second convolutional neural network comprises animage domain initial convolutional layer and an end convolutional layerfor processing the reconstructed image in an image domain.
 12. Themethod according to claim 11, wherein each convolutional layer includedin the image domain initial convolutional layer has an activationfunction, and the end convolutional layer has no activation function.13. A device for reconstructing a Computed Tomography (CT) image,comprising: a CT scanning apparatus configured to perform CT scanning onan object to be inspected to obtain projection data; a processorconfigured to: process projection data by using a first convolutionalneural network to obtain processed projection data, and perform aback-projection operation on the processed projection data to obtain areconstructed image, wherein the first convolutional neural networkcomprises a plurality of convolutional layers, process the reconstructedimage by using a second convolutional neural network to obtain aresultant image.
 14. The device according to claim 13, wherein the CTscanning apparatus is configured to perform one of the following:detector under-sampling scanning, sparse-angle scanning,intra-reconstruction scanning, finite angle scanning, and lineartrajectory scanning, and the first convolutional neural network is apooling layer-free convolutional neural network.
 15. The deviceaccording to claim 13, wherein the CT scanning apparatus is configuredto perform circular scanning or helical scanning, and the firstconvolutional neural network further comprises a plurality of poolinglayers disposed after respective convolutional layers, and a fullyconnected layer.
 16. The device according to claim 15, wherein theprocessor is further configured to: locally smooth the reconstructedimage by using the second convolutional neural network to obtain theresultant image.
 17. A non-transitory computer-readable medium havingcomputer programs stored thereon, which when being executed by aprocessor, cause the processor to perform the following steps:processing projection data by using a first convolutional neural networkto obtain processed projection data, wherein the projection data isobtained by performing CT scanning on an object to be inspected, and thefirst convolutional neural network comprises a plurality ofconvolutional layers; performing a back-projection operation on theprocessed projection data to obtain a reconstructed image; andprocessing the reconstructed image by using a second convolutionalneural network to obtain a resultant image.